Question

If the median of the distribution given below is $28.5$. Find the values of $x$ and $y$.

Class interval	Frequency	Cumulative frequency
0-10	5	5
10-2	x	5+x
20-30	20	25+x
30-40	15	40+x
40-50	y	40+x+y
50-60	5	45+x+y
Total	60

• A. $x=8$ and $y=7$
• B. $x=5$ and $y=5$
• C. $x=2$ and $y=9$
• D. $x=1$ and $y=2$

Answer 1

The correct option is A $x=8$ and $y=7$

Median $=28.5$ lies in the class interval $(20-30)$.
Then median class is $(20-30)$.
So, we have $l=20,f=20,cf=5+x,h=10,n=60$
Median $=l+\left\{\frac{\frac{n}{2}-cf}{f}\right\}\times h=28.5$
$\Rightarrow 28.5=20+\left\{\frac{30-(5+x)}{20}\right\}\times 10$
$\Rightarrow 8.5=\frac{25-x}{2}$

$\Rightarrow 17=25-x$

$\Rightarrow x=8$
Find the given table, we have
i.e., $x+y+45=60$ or $x+y=15$
$\Rightarrow y=15-x=15-8=7$, i.e., $y=7$